Evaluate Using Scientific Notation (710^28.510^4)/(510^3)

$\frac{7 \cdot 10^{2} \cdot 8.5 \cdot 10^{4}}{5 \cdot 10^{3}}$

Step 1

Multiply $7$ by $8.5$ .

$\frac{59.5 (10^{2} \cdot 10^{4})}{5 \cdot 10^{3}}$

Step 2

Multiply $10^{2}$ by $10^{4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{59.5 \cdot 10^{2 + 4}}{5 \cdot 10^{3}}$

Add $2$ and $4$ .

$\frac{59.5 \cdot 10^{6}}{5 \cdot 10^{3}}$

Step 3

Divide using scientific notation.

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{59.5}{5}) (\frac{10^{6}}{10^{3}})$

Divide $59.5$ by $5$ .

$11.9 \frac{10^{6}}{10^{3}}$

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$11.9 \cdot 10^{6 + 3 \cdot - 1}$

Multiply $3$ by $- 1$ .

$11.9 \cdot 10^{6 - 3}$

Subtract $3$ from $6$ .

$11.9 \cdot 10^{3}$

Step 4

Move the decimal point in $11.9$ to the left by $1$ place and increase the power of $10^{3}$ by $1$ .

$1.19 \cdot 10^{4}$

Evaluate Using Scientific Notation (7*10^2*8.5*10^4)/(5*10^3)